Multiobjective　differential　evolution　(DE)　algorithm　(MODE)　has　been　widely　used　in　multiobjective　optimization　problems.　However,　due　to　the　complex　feasible　regions,　the　optimization　efficiency　of　MODE　may　decrease　when　solving　constrained　multiobjective　problems.　It　is　challenging　to　promote　the　evolution　of　population　with　few　feasible　solutions.　In　this　article,　a　multistate-constrained　MODE　with　variable　neighborhood　strategy　(MSCMODE-VNS)　is　proposed　to　enhance　the　optimization　effectiveness　with　complex　feasible　regions.　First,　a　variable　neighborhood　DE　strategy,　based　on　a　specially　designed　convergence　indicator,　is　designed　to　accelerate　the　generation　of　feasible　solutions.　Second,　a　multistate　population　updating　strategy　with　a　comprehensive　solution　evaluation　mechanism　is　devised　to　update　the　population　of　the　next　generation　to　improve　the　performance　of　solutions.　Third,　the　convergence　analysis,　based　on　the　probability　theory,　is　derived　to　verify　the　effectiveness　of　the　proposed　MSCMODE-VNS　algorithm.　Finally,　experimental　results　indicate　that　MSCMODE-VNS　can　achieve　a　satisfactory　performance　on　three　benchmark　test　suites　and　two　real-world-constrained　multiobjective　problems.